THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Electromagnetic induction
The generation of an electromotive force in a circuit whenever the magnetic flux through it changes. Discovered by Faraday and Henry in 1831, it is the foundation of every electric generator, transformer, and inductive sensor ever built.
Electromagnetic spectrum
The full range of frequencies (or equivalently wavelengths) of EM radiation, from kilohertz radio to zettahertz gamma rays. All regions are the same physical phenomenon — classical EM waves — differing only in ω.
Electromagnetic wave
A self-sustaining coupled oscillation of electric and magnetic fields that propagates through vacuum at c = 1/√(μ₀ε₀). E, B, and k are mutually perpendicular. Maxwell's synthesis identified light itself as an electromagnetic wave.
Electromagnetic wave equation
The second-order PDE ∇²E = (1/c²)∂²E/∂t² (and identically for B), derived from Maxwell's equations in source-free vacuum. Its plane-wave solutions propagate at c = 1/√(μ₀ε₀).
Electromotive force (EMF)
The work per unit charge done by a source on charges as they move around a closed circuit, measured in volts. Despite the name, EMF is not a force; it is the energy-per-charge a battery, generator, or induction process supplies.
ellipse
Closed curve where the sum of distances from any point to two foci is constant.
elliptic integral
Integral involving square root of cubic/quartic polynomial; gives the exact period of a large-angle pendulum.
Elliptical polarization
The general polarisation state of a single-frequency EM wave: the E-vector traces an ellipse per cycle. Linear and circular polarisations are the two degenerate limits.
EM Lagrangian density
The Lorentz-invariant scalar L = −¼F_{μν}F^{μν} − A_μJ^μ from which all of classical electromagnetism follows. Euler-Lagrange recovers Maxwell's equations; gauge invariance via Noether gives charge conservation. The cleanest sentence in physics.
Energy cascade
Richardson's picture: energy injected at large scales is handed down, eddy by eddy, to smaller scales until viscosity dissipates it as heat.
Energy Conditions
The inequalities that demand 'gravity attracts' — the fuel the singularity theorems burn.
Ensemble
A conceptual collection of all microstates available to a system, weighted by probability — the bookkeeping device of statistical mechanics.
Enthalpy
H = U + PV, the energy bookkeeping appropriate to processes at constant pressure.
Entropy
The state function S with dS = dQ_rev/T — the quantity that stays constant on reversible paths and grows on every other.
Entropy of mixing
The entropy increase when distinct gases interdiffuse — positive even though no heat is added.
Eötvös parameter
The dimensionless ratio η = (m_g − m_i)/m_i quantifying the fractional difference between gravitational and inertial mass for a given material. Eötvös's torsion-balance experiments constrained η ≲ 10⁻⁹; modern Eöt-Wash and MICROSCOPE measurements push the bound to ≲ 10⁻¹⁵.
epicycle
Small circle whose center moves along a larger one; Ptolemy's device for saving uniform circular motion.
equatorial bulge
The excess of the Earth's equatorial radius over its polar radius (about 21 km), caused by the centrifugal deformation of rotation.
Equipartition theorem
Every quadratic degree of freedom carries an average energy of ½k_BT — the theorem that fixes heat capacities, and whose failures opened the door to quantum mechanics.
Equipotential
A surface on which the electric potential is constant. No work is done moving a charge along an equipotential, and the electric field is everywhere perpendicular to it.
Equivalence principle
Einstein's foundational GR axiom: no local experiment can distinguish a freely falling laboratory in a gravitational field from an inertial laboratory in flat spacetime. Comes in three increasingly strong forms — weak (m_g = m_i), Einstein (WEP + local Lorentz invariance + local position invariance), and strong (extends to self-gravitating bodies).
Ergosphere
The region outside a spinning black hole's horizon where standing still is impossible.
escape velocity
The minimum speed needed to escape a gravitational field: v_esc = √(2GM/r). For Earth's surface, ~11.2 km/s.
Euler angles
Three angles specifying the orientation of a rigid body in space relative to a fixed reference frame.
Euler-Lagrange equations
d/dt(∂L/∂q̇) = ∂L/∂q — the differential form of stationary action, equivalent to Newton's second law.
Event Horizon
The one-way causal boundary of a black hole: the surface past which no signal can ever return to the outside universe.
Extensive quantity
A property that scales with the size of the system — double the system, double the quantity.
Far-field zone
The region r ≫ λ surrounding an oscillating source where the field is an outgoing spherical wave with amplitude ∝ 1/r and time-averaged Poynting flux that transports energy irreversibly outward. Also called the radiation zone, Fraunhofer zone, or wave zone.
Farad
The SI unit of capacitance. One farad holds one coulomb of charge per volt of potential difference. Symbol: F.
Faraday cage
A conducting enclosure that blocks external static and low-frequency electric fields by redistributing charge on its surface.